FYKOS Year 36 Series 3 Problem 3 — bobsled · FYKOS 36 #36.3.3
Physics · mechanics
Problem
Matěj and David are sliding on bobsleds down the hill. The hill with a slope of α=29∘ turns into the horizontal ground at the bottom of it. Both of them started from rest from the same height. Matěj's bobsled always travels the same distance l on an inclined plane as well as in a horizontal part. Since the bobsled digs deeper into the snow at higher loads, assume the coefficient of friction to be proportional to the normal force as f(F)=kF, where k is a positive constant. Determine how many times Matěj will travel farther from the bottom of the hill than David if David's mass (including the bobsled) is 12% greater than Matěj's. Also, assume that bobsledders don't lose any energy at the bottom of the hill.